/**
 * 面试题47：礼物的最大价值
 */
public class Offer_47 {
    /**
     * 动态规划
     * <p>
     * 时间复杂度：O(row*col)
     * <p>
     * 空间复杂度：O(row*col)
     */
    public int maxValue(int[][] grid) {
        if (grid == null || grid.length == 0) {
            return 0;
        }

        int row = grid.length, col = grid[0].length;
        // dp[i][j] 表示走到 (i,j) 能拿到礼物的最大价值
        int[][] dp = new int[row][col];
        dp[0][0] = grid[0][0];
        // 初始化第一列
        for (int i = 1; i < row; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }
        // 初始化第一行
        for (int j = 1; j < col; j++) {
            dp[0][j] = dp[0][j - 1] + grid[0][j];
        }

        for (int i = 1; i < row; i++) {
            for (int j = 1; j < col; j++) {
                dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]) + grid[i][j];
            }
        }
        return dp[row - 1][col - 1];
    }

    public static void main(String[] args) {
        Offer_47 solution = new Offer_47();
        int[][] grid = { { 1, 3, 1 }, { 1, 5, 1 }, { 4, 2, 1 } };
        int ans = solution.maxValue(grid);
        System.out.println(ans);
    }
}
